The mechanism of spin and charge separation in one dimensional quantum antiferromagnets

TL;DR

This paper demonstrates that in one-dimensional quantum antiferromagnets, spin and charge separation cannot be described by slave particle methods within perturbation theory, and instead are represented by solitons, emphasizing the importance of exact constraints.

Contribution

It proves a no-go theorem showing slave boson and fermion representations fail to describe spin-charge separation in 1D strongly correlated systems, highlighting solitons as the true excitations.

Findings

Slave particle methods are inadequate for 1D spin-charge separation.

Excitations are solitons, not slave particles.

Phase diagram derived from non-perturbative fluctuation analysis.

Abstract

We reconsider the problem of separation of spin and charge in one dimensional quantum antiferromagnets. We show that spin and charge separation in one dimensional strongly correlated systems cannot be described by the slave boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations which carry the separate spin and charge quantum numbers are solitons. To prove this {\it no-go} result, it is sufficient to study the pure spinon sector in the slave boson representation. We start with a short-range RVB spin liquid mean-field theory for the frustrated antiferromagnetic spin-${1\over2}$ chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations non-perturbatively.